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    Re: lunars with and without altitudes
    From: Frank Reed CT
    Date: 2006 Nov 12, 00:21 EST
    George you wrote:
    "However, one skilled man could do the whole job:
    any additional calculation, if the job was done systematically,
    involved no more than an extra bit of time-averaging. The most logical
    sequence was to take a star (or Sun) altitude, then a Moon altitude,
    then some lunar distances, then a Moon altitude, then a star altitude,
    in a regular time-sequence like clockwork, so that the averaged times
    for all three sets of measurements were the same. That was how a
    lightly-officered merchant vessel would proceed"
    It's also worth mentioning that this procedure was outlined in most of the early 19th century navigation manuals like Bowditch. Assistants were not necessary. Then again, they were usually available aboard smaller vessels. There was a lot of cheap labor.
    Also, it works really well in practice. If you've never tried it, it takes relatively little discipline to arrange the set of sights so that the altitude pairs average nicely to the same time as the average of the lunars.
    And you wrote:
    "Asking for the calculated altitude to be within four arc-minutes of
    the truth may be a bit over the top, but it's not entirely
    unreasonable. The biggest effect would be on the parallax correction
    for a high Moon at about the same azimuth as the relevant star. With
    such an error, the resulting error in the parallax correction could be
    no more than about 4 arc-sec."
    Within +/-4 minutes of arc for the altitudes is correct when the lunar distance is about 40 degrees. Just a reminder on the "ninety degree miracle" business from two years ago: if the lunar distance is near 90 degrees, the altitude of the Moon can be wrong by a whole degree or more and it will have no significant effect on clearing the lunar distance. The other altitude should still be accurate to +/- 6 minutes of arc. If the other object's altitude is being used for a time sight, too, then the observer should try for maximum accuracy when measuring that altitude.
    If the lunar distance is short, you have to be more careful in the altitude. At a distance of ten degrees, an error of one minute in either altitude will yield a tenth of a minute error in the clearing process.
    When calculating altitudes, if that's the better option, it's no problem to calculate to the nearest arc second but they can still be in error by several minutes of arc. In this case, the source of error is transferred from the altitudes to the two inputs that determine those calculated altitudes: the DR latitude and the local apparent time (which is secondarily dependent on the DR longitude).
    42.0N 87.7W, or 41.4N 72.1W.

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